Revealing quantum Griffiths singularities inside the ferromagnetic phase

We present low-temperature inhomogeneous magnetic properties of the d-metal alloy Ni$_{1-x}$V$_x$ close to the quantum critical concentration $x_c \approx 11.6\%$ where the ferromagnetic transition temperature is suppressed to zero. The magnetization $M$ displays a singular dependence on the magnetic field $H$ not just in the paramagnetic phase ($x>x_c$) but also in the ferromagnetic phase ($x< x_c$). It is well described by a nonuniversal power law, $M -M_0 \sim H^\alpha$ with $M_0$ being the spontaneous magnetization. The exponent $\alpha$ is strongly $x$-dependent, approximately symmetric in $x-x_c$, and decreases to zero at $x_c$. Muon spin rotation experiments in longitudinal magnetic fields and zero fields in the ferromagnetic phase demonstrate inhomogeneous magnetic order and indicate the presence of dynamic fluctuating magnetic clusters. A similar cluster fraction can be estimated by both bulk of local probes that becomes significant close to $x_c$. These results provide strong evidence for a quantum Griffiths phase on the ferromagnetic side of the quantum phase transition.